(1) Technical Field of the Invention
The present invention relates generally to the field of measurement and testing instrumentation and in particular to sensors for the measurement of shear stresses in fluid flows.
(2) Description of the Prior Art
The transport of mass, momentum and concentration in a shear flow are governed by the stress sensor field. These flow characteristics produce direct and shearing stresses which owe their origin to viscosity. In potential flow theory, a fluid is "frictionless" with shear stress assumed to be zero, thereby allowing solutions to the flow equations as only direct stresses need to be considered. Potential flow solutions, while providing some general design information for airfoils or hydrofoils, are unsatisfactory for design problems involving high lift, laminar flow, stall, and other circumstances where boundary layer flow is important. Additionally, in a turbulent flow, the stress components have additionally the "Reynolds" or apparent stresses coming from the fluctuating velocities. These stress components are time dependent. For purposes of the invention herein, these apparent stresses are not considered.
Navier-Stokes equations are the fundamental equations of motions of a fluid. Using these equations, the shear stress components are not treated directly. They are derived in terms of rate of strain, that is, spatial velocity derivatives (see "Boundary-Layer Theory" by Schlichting 1979 7th ed. p. 58, McGraw-Hill, N.Y.). All measurements of shear stresses are made by measuring the instantaneous velocity field. These measurements must be carried out to a high degree of resolution as the derivatives are very Sensitive to such resolution. Using these methods, solution of the equations is dependent on the assumption that shear stresses are equal where the stress tensor elements differ only in the order of subscripts, that is, .tau..sub.xy =.tau..sub.yx. Using this assumption, the stress tensor matrix is symmetrical in relation to its principal diagonal. Without this assumption, the complexity of the flow and corresponding equations preclude solutions of the Navier-Stokes equations.
The development of devices which apply hydrostatic forces to a fluid, causing local movement proportional to the fluid volume, result in invalid results using the symmetric matrix assumptions. These devices include magneto-electrostatic drive systems which are currently under development for submarine or other undersea vehicle propulsion systems. In analytic development of such systems, it is necessary to measure shear stresses within and across the boundary layer. Shear stresses must be measured not only at a flow surface, but also throughout the thickness of the boundary layer.
Currently, the shear stresses are measured by three methods (or their variations): (1) hot-wire anemometry, (2) multiple component laser Doppler velocimetry (LDV) and (3) particle image velocimetry (PIV). The first method requires a precise calibration and only measure is shear stress indirectly. The latter two methods require no calibration and both measure the velocities directly. Once measurements are complete, the shear stress is then derived from the spatial derivatives of the measurements.
All these techniques have many drawbacks. Both the hot-wire or film anemometry are indirect methods. Both techniques are subject to temperature drift. Additionally, each is subject to physical and thermal interference caused by the probe. Further, the sensors are very fragile.
Further problems arise from the analytical assumptions involved in the derivation of the stresses from the measured voltage output. Also, the natural response of the sensor is nonlinear. Due to these reasons, the results can have uncertainties of 20% or even higher and the results are somewhat ambiguous. In the presence of an electric or magnetic field, the hot wire reliability may be affected due to induced current or voltage. Further, hot wire anemometry is also insensitive to flow direction.
The LDV technique also has many limitations. The probe volume is usually large. As a result, near wall measurements are difficult due to fringe interference, often requiring seeding of the flow. Without an adequate seeding, data can be lost and interpretation of the data Becomes ambiguous. Another unresolved problem of the technique is velocity bias. Further, alignment difficulties, vibration isolation, the difficulty of access through optical quality windows and the sheer bulk of the attendant laser and optics are also impediments. It is difficult, if not impossible to use it in a field test or in flight. When the flow field is unsteady, the burden of measurements in hot-wire and LDV which are point methods, increases greatly.
The PIV technique also has its drawbacks. Here, PIV includes the technique called holo-cinematography velocimetry (HCV). Currently, PIV is still under development. It is primarily being developed in low speed water flows where the Reynolds number is also low. It is extremely computer intensive. Unambiguous methods of tracking the particles are yet to be developed. The fluid must be seeded with appropriate neutrally buoyant spheres. This requirement precludes the use of the PIV technique in the ocean or in flight. It needs involved optics and photography. Furthermore, mobility of the technique is limited.
Alternatively, in laminar flows, the stress field can be simulated by Direct Numerical Simulation of the Navier-Stokes Equations. Although they are extremely well calibrated and verified over the years, two aspects of these equations should be noted which are in contrast to the present invention. First, the so called second stress factor of proportionality is obtained by Stokes's hypothesis and second, the stresses are indirectly derived from velocity derivatives.